Semiclassical description of spin ladders

TL;DR

This paper analyzes spin ladders using semiclassical methods, revealing how the spin gap depends on inter-chain coupling and spin values, supported by Monte Carlo simulations.

Contribution

It introduces a semiclassical approach to spin ladders via nonlinear sigma models, detailing the gap behavior for different coupling regimes and spin configurations.

Findings

Spin gap exists for nonzero coupling if sum of spins is integer.

Gap drops sharply as inter-chain coupling increases for integer spins.

Monte Carlo simulations support the analytical predictions.

Abstract

The Heisenberg spin ladder is studied in the semiclassical limit, via a mapping to the nonlinear $\sigma$ model. Different treatments are needed if the inter-chain coupling $K$ is small, intermediate or large. For intermediate coupling a single nonlinear $\sigma$ model is used for the ladder. Its predicts a spin gap for all nonzero values of $K$ if the sum $s+\tilde s$ of the spins of the two chains is an integer, and no gap otherwise. For small $K$, a better treatment proceeds by coupling two nonlinear sigma models, one for each chain. For integer $s=\tilde s$, the saddle-point approximation predicts a sharp drop in the gap as $K$ increases from zero. A Monte-Carlo simulation of a spin 1 ladder is presented which supports the analytical results.